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带三次项的非线性四阶Schrödinger方程的一个局部能量守恒格式

林超英1, 黄浪扬1, 赵越2, 朱贝贝2   

  1. 1. 华侨大学数学科学学院, 福建泉州 362021;
    2. 中国科学院数学与系统科学研究院, 北京 100190
  • 收稿日期:2014-08-06 出版日期:2015-02-15 发布日期:2015-03-10
  • 通讯作者: 黄浪扬, Email: hly6@163.com.
  • 基金资助:

    国家自然科学基金资助项目(11271171,11371357),福建省自然科学基金资助项目(2011J01010)和华侨大学中青年教师科研提升资助计划项目(ZQN-PY201).

林超英, 黄浪扬, 赵越, 朱贝贝. 带三次项的非线性四阶Schrödinger方程的一个局部能量守恒格式[J]. 计算数学, 2015, 37(1): 103-112.

Lin Chaoying, Huang Langyang, Zhao Yue, Zhu Beibei. A LOCAL ENERGY CONSERVATIVE SCHEME FOR THEFOURTH-ORDER SCHRÖDINGER EQUATION WITH CUBIC NONLINEAR TERM[J]. Mathematica Numerica Sinica, 2015, 37(1): 103-112.

A LOCAL ENERGY CONSERVATIVE SCHEME FOR THEFOURTH-ORDER SCHRÖDINGER EQUATION WITH CUBIC NONLINEAR TERM

Lin Chaoying1, Huang Langyang1, Zhao Yue2, Zhu Beibei2   

  1. 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    2. Academy of Mathematics and Systems Science, CAS, Beijing 100190, China
  • Received:2014-08-06 Online:2015-02-15 Published:2015-03-10
本文构造了带三次项的非线性四阶Schödinger方程的一个局部能量守恒格式.证明了该格式是线性稳定的,且能保持离散的整体能量守恒律及离散的电荷守恒律.最后通过数值算例验证了理论结果的正确性.
In this paper, a local energy conservative scheme is constructed to solve the fourth-order Schrödinger equation with cubic nonlinear term. We prove that the scheme is linear stable and preserves the discrete global energy and discrete charge. Finally, the correctness of the theoretical results is demonstrated by the numerical examples.

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